Simplification Theorems

(X + Y’)Y = XY

XY + Y’Y = XY + 0 = XY

XY’ + Y = X + Y

(using the second distributive law)

XY’ + Y = Y + XY’ = (Y + X)(Y + Y’)

= (Y + X)·1 = X + Y

XY + XY’ = X

XY + XY’ = X(Y + Y’) = X·1 = X

X + XY = X

X(1 + Y) = X·1 = X

(X + Y)(X + Y’) = X

(X + Y)(X + Y’) = XX + XY’ + YX + YY’

= X + X(Y’ + Y) + 0

= X + X·1

= X

X(X + Y) = X

X(X + Y) = XX + XY = X·1 + XY

= X(1 + Y) = X·1 = X

Previous slide

Next slide

Back to first slide

View graphic version